Summary: An identifying code \(C\) is a subset of the vertices of the square grid \({\mathbb Z}^2\) with the property that for each element \(v\) of \({\mathbb Z}^2\), the collection of elements from \(C\) at a distance of at most one from \(v\) is nonempty and distinct from the collection of any other vertex. We prove that the minimum density of \(C\) within \({\mathbb Z}^2\) is \(\frac{7}{20}\).